BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.6, Problem 64E

(a)

To determine

The function f that models the purchase price of the cell phone as function of the regular price x.

Expert Solution

Answer to Problem 64E

The value of the function f is f(x)=0.8x .

Explanation of Solution

Given:

The discount applies on price of cell phone is 20%.

Calculation:

The price of cell phone is x.

The discount applies on price of cell phone is 20%.

Since the function f that models the purchase price of the cell phone as a function of the regular price x, therefore the function f is written as the difference between actual price of cell phone and discount,

f(x)=x20%ofx=x0.20x=0.8x

Thus, the value of the function f is f(x)=0.8x .

(b)

To determine

The function g that models the purchase price of the cell phone as a function of the sticker price x.

Expert Solution

Answer to Problem 64E

The value of the function g is g(x)=x50 .

Explanation of Solution

Given:

The function g is the function that models the purchase price of the cell phone as a function of the sticker price x.

The amount of coupon is $50 .

Calculation:

Since the function g is the function that models the purchase price of the cell phone as a function of the sticker price x, therefore the function g is written as the difference between actual price of cell phone and the amount of the coupon,

g(x)=x50

Thus, the value of the function g is g(x)=x50 .

(c)

To determine

The values of fg , gf , and the composition function which gives less purchase price.

Expert Solution

Answer to Problem 64E

The value of fg is (fg)(x)=0.8x40 and the value of gf is (gf)(x)=0.8x50 . The purchase price from the composite function gf is less.

Explanation of Solution

Given:

From part (a), the value of function f is given below,

f(x)=0.8x (1)

From part (b), the value of function g is given below,

g(x)=x50 (2)

Calculation:

The composite function fg is expressed as,

(fg)(x)=f(g(x))

From equation (2), substitute x50 for g(x) in above expression,

(fg)(x)=f(x50) . (3)

Substitute x50 for x in equation (1), to find the value of f(x50) ,

f(x50)=0.8(x50)=0.8x40

Substitute 0.8x40 for f(x50) in equation (3), to find the value of fg ,

(fg)(x)=0.8x40

The purchase price from the composite function fg is 0.8x40 .

The composite function gf is expressed as,

(gf)(x)=g(f(x))

From equation (1), substitute 0.8x for f(x) in above expression,

(gf)(x)=g(0.8x) (4)

Substitute 0.8x for x in equation (2), to find the value of g(0.8x) ,

g(0.8x)=0.8x50

Substitute 0.8x50 for g(0.8x) in equation (4), to find the value of gf ,

(gf)(x)=0.8x50

The purchase price from the composite function gf is 0.8x50 .

The purchase price from the composite function gf is less than the purchase price from the composite function fg .

Thus, the value of fg is (fg)(x)=0.8x40 and the value of gf is (gf)(x)=0.8x50 . The purchase price from the composite function gf is less.

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